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Math Help - z or t test ANOVA

  1. #1
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    Smile z or t test ANOVA

    I have a question about when I should use what...

    ln (p/1-p) = B0 + B1 * age + B2 * civil status
    n=100

    Show with a statistical test that/if age and civil status affect the outcome of y.

    B SE
    Age -0,0632 0,0196
    Civil status -0,0427 0,4545
    Constant 2,8190 0,9335

    So my question is if I should use a or b
    a) z=B/SE =-0,0632/0,0196=-3,22 3,22>1,96 can show that it effects
    =-0,0427/0,4545=-0,094 0,094<1,96 cant show that it effects

    H0: B1=o B2=0
    H1: B1≠0 B2≠0
    b) t=b1-B1/sb1 =-0,0632-0/0,0196=-3,22
    =-0,0427-0/0,4545=-0,094
    tkrit= ?

    Thanks in advance!!!
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  2. #2
    Super Member ILikeSerena's Avatar
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    Re: z or t test ANOVA

    Hi emme1!

    This is a multiple linear regression where you test the individual coefficients with a t-test.
    Btw, ANOVA is not involved (there are no variances that are being analyzed).

    For the first coefficient, you have:

    H0: B1=0
    H1: B1≠0

    It's a t-distribution with n-3=100-3=97 degrees of freedom (generally df=n-p-1, where p is the number of parameters).

    You get (slight modification of what you wrote):
    t=(b1-0)/SEb1=-0,0632-0/0,0196=-3,22

    Assuming an alpha of 5%, your critical t-value is t*=1,98.
    (As you can see this is quite close to the 1,96 critical z-value you already had.)

    Since t = -3,22 < -1,98, it follows that H0 can be rejected.

    So yes, age has a significant effect on the outcome.


    The method for the other coefficient is the same.
    Last edited by ILikeSerena; January 6th 2013 at 09:50 AM.
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  3. #3
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    Re: z or t test ANOVA

    Thanks a lot!!
    and thank you for helping me with the df!

    I just got the "correct answer" and they used the z-test.
    hmm... When do you use the z-test like I wrote above?
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  4. #4
    Super Member ILikeSerena's Avatar
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    Re: z or t test ANOVA

    Hmm, the critical difference between a t-test and a z-test is knowledge about the standard deviation of the population parameter.

    Wait, I'm just realizing that you are apparently testing proportions.
    That is something that can be treated as having a known standard deviation.
    The point being that the corresponding binomial distribution can be approximated by a normal distribution with a standard deviation that can be calculated.

    To be honest, I'm not exactly sure of all the details, but it might be okay to do a z-test then.

    Btw, as you've already seen, it matters not at all.
    The critical values are very close, and the scores are way different.
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  5. #5
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    Re: z or t test ANOVA

    True!
    So I guess both ways are correct?

    I have seen both, but I just assumed that one of them was wrong... it's tricky
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  6. #6
    Super Member ILikeSerena's Avatar
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    Re: z or t test ANOVA

    From a practical point of view, both are just fine.

    From a theoretical point of view, you should take a look at your notes, or your book.
    It probably contains a worked example or something that shows exactly how you're supposed to do it... for a logistic regression in multiple variables.
    (I'd tell you, but wikipedia does not appear to contain all the details.)
    Last edited by ILikeSerena; January 6th 2013 at 11:10 AM.
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